Sparke & Gallagher; 2nd edition
1. Introduction
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1.1 Stars
Why stars important; (bolometric) luminosity; distances, radii;
Properties, spectra, chemical abundances; evolution;
Spectra of galaxies are a composite;
Elements: H and He, and the "metals"; astronomers periodic table
Metallicity scale - relative and logarithmic; abundance patterns
Metals are a source of opacity in a star
Cepheids. r-process and s-process. Binaries.
The magnitude systems and the distance modulus;
Sky transparency; bandpasses; typical filters; colors
1.2 Our Milky Way
Main constituents;
Exponential scale height and scale length; thin and thick disks
Orbits of GC's, stars in the disk; DM halo; metallicity;
Local stellar density. Gas: ionized, neutral, molecular.
Recombination cascade, Balmer lines (n=2) in HII regions,
(recall Balmer limit in stars). Lyman-alpha line.
Collisional and photo ionization; forbidden lines, as diagnostics
Fine structure lines, hyperfine, 21 cm line;
Molecular lines: vibrational and rotational transitions; masers
Bremsstrahlung, synchrotron radiation
Dust obscuration, opacity, optical depth; 1/cos law
Coordinate systems: RA and Dec (1950 or 2000 equinox); l and b
1.3 Other galaxies
1936, The Realm of the Nebulae; Ellipticals, Lenticulars, Spirals, Irr;
cD galaxies; most numerous and least luminous: dEll, dSph. Starburst.
Surface brightness, isophotes, Holmberg radius (26.5mag/arcs^2; 1% sky)
Schechter luminosity function, L_star
1.4 Galaxies in the expanding Universe
Redshift; 1929 Hubble Law, and Hubble "constant"; Hubble time.
Radial velocity, peculiar velocities of galaxies.
Critical density, the future of expansion; age of the Universe.
Expansion age, stellar ages, dynamical timescales (GCs), etc.
1.5 The pregalactic era: a brief history of matter
Big Bang Nucleosynthesis (mainly Helium production)
Thermal history (early Universe)
Recombination/decoupling, Cosmic Microwave Background (CMB)
Present day Extragal. background radiation across the EM spectrum
2. Mapping Our Milky Way
========================
2.1 The Solar neighborhood
Measuring distances to stars: direct absolute method: trig parallax;
the rest of distance scale is based on relative distance indicators.
Distance modulus; various ways of using HR diagram as a dist. ind.
How do we observationally construct (present day) Luminosity fcn for stars?
How do we convert present day LF to initial LF?
How do we convert initial LF to initial mass function, the IMF?
2.2 The stars in the Galaxy
Distances from motions; Spectroscopic parallax.
Number density of stars in the disk - exponential distribution;
Disk's scale length and scale height for different populations
Velocity dispersion of stars
(skip p.72, p.74, skim 2.2.3)
IR view: the bulge and nucleus:
Evidence for bar; bar's metallicity, rotation.
Star clucters at Galactic center; evidence for central black hole
2.3 Galactic Rotation
Differential rotation as seen in the Solar neighborhood
Local Standard of Rest (LSR)
Measuring the Galactic rotation curve; Oorts constants A and B
Measuring distribution of dark matter
2.4 Milky Way meteorology: the interstellar gas
Why molecular H is hard to detect; CO & other tracer of (dense) gas
Kinematic distance to HI in the disk
High Velocity Clouds - distances, masses hard to estimate
Absorption lines due to warm gas. Galactic wind (very hot gas)
ISM is a multiphase medium: see the summary in Table 2.4
All phases are in approximate pressure balance!
Other features of the ISM: magnetic field, cosmic rays, turbulence.
Energy input from stars to ISM: what does this energy do?
Dust ~ 1% of ISM mass; PAHs are 10% of ISM mass.
In dense gas, metals occur preferentially in grains, not dust.
Hydrogen molecules are made preferentially on grain surfaces.
Cooling curve, Fig. 2.25, and Table 2.5.
(skip pp. 107-109; we'll do these at some later time).
3. The Orbits of Stars
======================
3.1 Motion under gravity: weighing the Galaxy
The main goal of this section is to derive the Virial Theorem, eq.(3.44).
Applied to a system in steady state (not changing/evolving rapidly),
VT states, 2*[Total Kinetic Energy]+[Total Potential Energy]=0.
A collection of point masses (say, stars) in purely Newtonian set-up.
Potential Phi due to all the masses, eq.(3.4).
Force on a particles is the gradient of the potential, eq.(3.5).
Poisson equation: The Laplacian of Phi gives density, eqn.(3.6-3.9).
Newton's Theorems on p.114 (skip p.115).
Potential in a spherically symmetric system is given by eq.(3.21).
Energy and angular mom. of particles in a time-independent potential.
Total energy of an isolated star cluster, eq.(3.34).
Virial expression if the moment of inertia does not change.
Application of VT to astrophysical systems.
3.2 Why the Galaxy isn't bumpy: two-body relaxation
Relaxation - a process by which a system attains equilibrium and
erases information about its initial state.
3 types of dynamical relaxation:
[1] close (few, but strong) encounters,
[2] distant (weak, but frequent) encounters,
[3] changes in global potential (violent relaxation).
Impulse approximation; crossing time & relaxation time;
evaporation, mass segregation, core collapse in stellar systems.
3.3 Orbits of disk stars: epicycles
Orbits in axisymmetric potentials; particle's L_z ang.mom. conserved.
Motion in the R direction, the effective potential. Motion in the z-dir.
Harmonic oscillator solutions for R and z directions.
Galactic motion epicycles and Ptolemy's epicycles; two special cases:
Keplerial (point-mass) mass distribution & uniform mass distribution.
(you can skip p.140 and asymmetric drift)
3.4 The collisionless Boltzmann equation (CBE)
In the absence of collisions (which change velocities abruptly) the
flow of particles in 6D phase-space is continuous (no jumps). CBE is
a continuity equation in phase-space, for collisionless systems.
Moments of CBE; for example, eq.(3.90), which is an eqn. of motion.
(Skip 3.4.2)
4. Our backyard: The Local Group
================================
4.1 Satellites of the Milky Way
The two Magellanic Clouds; both can be classed as Irr;
both have high star formation rates. Maps at different wavebands.
Magellanic Stream, large angular extent on the sky; has HI, but no stars.
Star formation histories of the LMC and SMC. RR Lyrae and Cepheids.
Dwarf spheroidals vs. Globular Clusters: similarities and differences.
Tidal forces; effective potential in a rotating frame; Jacobi constant.
Lagrange points as stationary points in rotating systems
dominated by two massive bodies.
4.2 Spirals of the Local Group
Two main spirals: M31, similar to the Milky Way.
There are no (normal) ellipticals in the Local Group.
Disk warping in all 3 spirals; observed in HI gas and stars in M31.
M33, its properties, and nucleus.
This is a short section, so it does not need to fill the whole hour.
(LLRW will provide additional material.)
4.3 How did the Local Group galaxies form?
Galaxies collapse from small overdensities in the early Universe,
after recombination (production of the Cosmic Microwave Background CMB).
Galaxies acquire rotation through mutual tidal torques.
Galaxy formation proceeds hierarchically; formation of the main potential
well (i.e. DM halo) and formation of stars need not happen at the same time.
Formation of Globular Clusters. Eggen, Lynden-Bell, Sandage (1962) model.
Sagittarius Dwarf, and ongoing accretion of matter by the Milky Way.
The build-up of heavy elements: the relation between age and metallicity
is not always simple. A drastically simplified model: closed-box model,
and its consequence, the G-dwarf problem. Solutions: pre-enrichment, and
continuous inflow of metal-poor gas (open box model).
Oxygen, Silicon, Magnesium made mostly by SN Type II (core collapse);
Iron made mostly by SN Type Ia (WD in a binary)
4.4 Dwarf galaxies in the Local Group
Dwarf elliptical
Dwarf spheroidals
Dwarf irregulars
M32; V/sigma as a measure of 'coldness'
4.5 The past and the future of the Local Group
Estimating the mass of the Local Group using the dynamics of the
two largest galaxies, and assuming that their relative orbit is
mostly radial (not circular). Include problems 4.12 and 4.13 in
your discussion. (LLRW will fill in the remainder of the hour.)
5. Spiral and S0 galaxies
=========================
5.1 The distribution of starlight
(skip 5.1.1)
Galaxies' surface brightness distribution - contributions from
bulge and disk; isophotes. Effects of dust and inclination.
Exponential surface brightness profile; scale length.
Changes in properties from S0 to Sd.
Low Surface Brightness Galaxies (LSBs); have lots of HI gas;
they are forming stars at a low rate.
Spirals in the IR, optical, UV - what is seen at different wavelengths?
5.2 Observing the gas
(skip 5.2.1)
Emission from optically thin gas.
Self-shielding of gas may introduce an upper limit on observed
column density of HI.
Molecular vs. atomic gas in disks: different distributions
M(HI)/L_B ratio as an indicator of gas-richness.
Cases of unusual HI gas dynamics: retrograde disks, and polar rings.
5.3 Gas motions and the masses of disk galaxies
"Spider" diagrams, like fig.5.13. Explanation of the pattern.
Rotation curve decomposition: contributions from bulge, disk, halo.
Fig. 5.20. Maximum-disks model.
Hubble parameter dependence of Luminosity, Mass, and M/L ratio.
The Tully-Fisher relation; HI line profile, why the double-horn shape?
5.4 Interlude: the sequence of disk galaxies
Classification of disk galaxies; spectra of different types of spirals
5.5 Spiral arms and galactic bars
5.5.1: The pitch angle of spiral arms;
Grand design vs. flocculent spirals; spirals arms in barred spirals.
Leading vs. trailing arms; locating dust lanes can tell these apart.
What are spirals arms: material vs. density wave
5.5.2: Three (not mutually exclusive) theories of spiral structure:
(1) Self-proparating star formation coupled with differential rotation,
(2) Kinematic spiral pattern produced by elliptical orbit shapes, with
ellipses' position angle changing with radius;
(3) Density wave spiral structure - can exist only between inner and outer
Lindblad resonances in the disk (on either side of the corotation rad.)
Stability criterium in the disk; Toomre Q parameter, eq.(5.12)
Bars: material, not density wave structures; lie within corotation radius
5.6 Bulges and centers of disk galaxies
The most general shape for bulges is triaxial.
MW's and M31 bulges are metal-rich compared to disks; bulge star ages > several Gyr
Galaxies are redder closer to the center.
V/sigma~1; bulges are "fast rotaters".
The Sersic projected brightness profile, parameterized by n; n=4 is deVaucouleurs.
Effective radius and its relation to disk's scale length.
Bulge formation: various hypotheses.
Dense central (nuclear) star clusters; infall of gas and ongoing star formation.
Active Galactic Nuclei, supermassive black holes.
6. Elliptical galaxies
======================
6.1 Photometry
General 3D shape of an elliptical is the same as for bulges: triaxial.
Ellipticals span an order of magnitude in luminosity.
Isophotes: ellipticity and position angle, as a function of radius.
Sky-projection effects; E0, E1, ... E7 designation. Sersic empirical fit.
Central brightness profiles and seeing; cusps and cores.
cD galaxies at centers of galaxy clusters; their brightness profiles.
Relation between central brightness and total brightness.
(Skip 6.1.1.)
Twisting isophotes and triaxiality. Boxy and disky isophotes.
6.2 Motions of the stars
Absorption spectral lines and orbits of stars.
Faber-Jackson relation, the Fundamental Plane (FP). Relation to Tully-Fisher.
(Skip p.259)
How we deduce that ellipticals have anisotropic velocity dispersions.
Violent relaxation vs. two-body relaxation.
Stellar orbits; example of a triaxial harmonic oscillator.
Different types of orbits.
6.3 Stellar populations and gas
Spectra of galaxies of different stellar ages: compare Fig. 6.17 and 6.18.
Smaller ellipticals probably have younger (or metal poorer) stellar populations.
Redder galaxies are brighter, Fig. 6.19.
Massive galaxies have higher metallicities.
From Section 4.3:
Oxygen, Silicon, Magnesium - from SN Type II (core collapse => older stellar pops);
Iron - from SN Type Ia (WD in a binary, => younger stellar populations).
X-rays: various sources
Gas: little of warm, cool gas; some dust. Hot ionized gas exists.
Globular Clusters: two populations, old & blue, and younger & redder.
6.4 Dark Matter and Black Holes
Amount of dark matter as indicated by the M/L ratios.
Dymanics of outer region, using Globular Clusters, given M/L ~ 50.
Central Black Holes; measuring their masses.
Relation between BH mass and galaxy's velocity dispersion.
7. Galaxy Groups and Clusters
=============================
7.1 Groups: the homes of disk galaxies
Groups with and without ellipticals; X-rays from galaxy groups.
Measuring masses: dynamics and X-rays, both assume equilibrium.
Dynamical friction: slowing down of galaxies by grav interactions.
Galaxy interactions lead to increased star formation rate; Starbursts.
Long term prognosis for the Local Group, and other galaxy groups.
7.2 Rich clusters: the domain of S0 and Elliptical galaxies
Morphology-density relation in galaxy clusters.
Intra-cluster stars; planetary nebula and their OIII[5007] line.
Typical masses, sizes and M/L ratios of clusters.
X-ray emitting gas in clusters; similar to that in groups and elliptical galaxies.
Metallicity of this hot gas; why so high?
X-ray emitting gas contains a large fraction of baryons in today's Universe,
but not all.
7.3 Galaxy Formation: nature, nurture, or merger?
Formation of stars in a galaxy, and formation of galaxy are not the same thing.
Old galaxies (like MW) can have new stars, while new galaxies (ellipticals
assembled recently) can be composed of old stars.
Ellipticals are probably products of mergers of smaller galaxies.
Spirals with extended disks did not undergo any major mergers recently.
What happens to gas in a merger.
7.4 Intergalactic Dark Matter: gravitational lensing
Lensing deflection angle for a point source lens, eq.(7.13).
Einstein ring radius. Microlensing - when multiple images are unresolved.
Magnification of an image is proportional to the area it subtends on the sky.
Lensing potential (skip p.307-308).
Critical surface mass density for lensing, eq. (7.26).
Comparing cluster mass estimates using X-rays and using lensing.
(Skip p.311 and the top of p.312.)
Weak lensing (no multiple images are produced), instead, the shearing (distortion)
of images is measured. Weak lensing by clusters; weak lensing by galaxies.
8. The large-scale distribution of galaxies
============================================
8.1 Large Scale Structure (LSS) today
The "cosmic web": walls, filaments, voids.
Looking at the Universe through our galaxy: zone of avoidance.
Distance indicator for <20Mpc: surface brightness fluctuations method.
Distance indicator for >50Mpc: redshift (peculiar motions are small).
Using redshifts as distance proxies introduces distortions in LSS maps.
Clustering of spirals vs. elliptical galaxies; morphology-density relation, again.
Biasing in galaxy distribution.
Clustering of galaxies as measured by the correlation function.
(Skip: from eq.(8.3) up to and including Problem 8.7.)
8.2 Expansion of a homogeneous Universe
Homogeneity and isotropy. Curvature: open, flat, closed. Comoving coordinates.
The meaning of redshift and Hubble parameter in terms of the scale factor.
Newtonian cosmological equation of motion, eq.(8.15) & (8.20); energy equation, eq.(8.17).
Stuff (various components) making up the Universe: cold matter, radiation, vacuum energy.
Critical density, and the Omega parameter.
Brief expansion history of the Universe: first radiation dominated, later matter dominated.
(Skip 8.2.1)
8.3 Observing the earliest galaxies
Very distant objects appear fainter because of cosmological redshifting of radiation,
but have larger angular size.
Olbers paradox: Universe is not infinitely old.
Angular size and luminosity distances (concepts only, no equations), Figure 8.11.
Bolometric surface brightness and its decrease with redshift, Figure 8.10.
(Skip most of p.338-339.)
Apparent magnitude of distant objects: k-corrections and the evolution term, eq.(8.45).
Photometric vs. the usual spectroscopic redshift.
(Skip Section 8.3.3.)
8.4 Growth of structure: from small beginnings
Density fluctuations in DM during the epoch of recombination translate into
temperature fluctuations of the "released" radiation --> CMB.
CMB fluctuations can be analyzed using spherical harmonics. The location of
the first peak in the CMB fluctuation power spectrum corresponds to the size
of the horizon (size of visible Universe) at the time of recombination.
Peculiar velocities of galaxies are due to the density fluctuations in the
DM distribution. Local example: Virgocentric infall. Local flow is "cold".
(Skip 8.4.3 and 8.4.4)
Tidal torques.
8.5 Growth of structure: clusters, walls, and voids
Jeans mass. WIMPs.
Collapse of spherical perturbations; virial radius in terms of overdensity.
(Skip 8.5.4)
9. Active Galacti Nuclei and the early history of galaxies
===========================================================
9.1 AGN
Classification of AGN.
Seyfert galaxies; Radio galaxies; Quasars.
(Skip 9.1.3)
9.2 Fast jets in AGN, microquasars, and gamma-ray bursts
(Apparent) superluminal motion of blobs in jets.
The jet approaching us is brighter because its radiation is
relativistically beamed; the receding jet appears much dimmer.
Microquasars: accretion disks around stellar mass compact objects.
Why discs around stellar mass BHs are hotter than those around supermassive AGN.
Gamma-ray bursts: duration, energy output; originate in stellar SN explosions;
opening angle of the jet; afterglows at longer wavelengths. GRBs as standard candles?
9.3 Intergalactic gas
Neutral hydrogen clouds along the lines of sight to QSOs produces absorption lines
at wavelengths which depend on the clouds' redshift. Clouds have some metals too.
Three types of clouds, according to their Hydrogen column density:
Lyman-alpha (Lya), Lyman limit (LyL), Damped Lyman-alpha (DLA).
The collection of all these makes us the "Lyman alpha forest" in QSO spectra.
Neutral gas fraction in Lya clouds can be very low. DLAs could be parts of galaxies.
Metallicity evolution with redshift.
Gunn-Peterson effect and the ionization state of the Universe with redshift.
9.4 The first galaxies
At higher redshifts we see mostly protogalactic fragments; not as many well formed galaxies.
Galaxy luminosity function at different redshifts, fig. 9.15.
Lyman break galaxies: look for objects that disappear in certain filters,
as 912A break moves into that filter.
Detecting early galaxies through their dust emission in the submm part of the spectrum.
Global star formation history of the Universe, fig. 9.17.